Guardat en:
| Autor principal: | |
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| Format: | Recurso digital |
| Idioma: | anglès |
| Publicat: |
Zenodo
2025
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| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.17354014 |
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Taula de continguts:
- <p><strong>From Physics as Computation to State-Parallel Computing</strong> develops the theoretical and semantic foundations of the State-Parallel Computing (SPC) paradigm, building upon the conceptual framework introduced in "State-Parallel Computing: Physical Governance as the Third Paradigm."</p> <p>This work formalizes computation as <strong>governed physical evolution</strong> on a state manifold Φ, constrained by a feasibility mask M, and evolved by a governed semigroup {Λₜ}. Within this framework, <strong>correctness becomes a property of physical invariance</strong> rather than post-execution verification.</p> <p>The paper defines both <strong>denotational and operational semantics</strong> for SPC. Denotationally, meaning corresponds to feasible ω-limit sets; operationally, execution unfolds through the <strong>Compilation–Iteration–Projection–Recovery (CIPR) cycle</strong>, linking compilation choices to runtime physics. Key results include the <strong>No-Bypass invariance theorem</strong>, Lyapunov-based correctness, exponential convergence rates, and ISS-type robustness under tangent perturbations.</p> <p>By unifying <strong>viability theory, projection dynamics, and Lyapunov stability</strong>, SPC establishes a mathematical contract between semantics and physical law—providing the rigorous basis for compiler and runtime design in hybrid physical substrates.</p> <p><strong>Relationship to Series:</strong> This paper serves as the <strong>semantic foundation</strong> for the SPC framework introduced in the first installment, completing the theoretical arc from paradigm definition to formal semantics.</p>